Pretty much anyone can install WordPress on their host's server and be blogging pretty quickly. As such I won't go into the details of that process as it is well documented all over the web. My focus here is to highlight some cool things and share some customization and testing tips that only experienced webmasters are likely to already know.
Unless you're happy blogging using WordPress right out of the box using its pre-installed themes, you'll likely want to do some customizing at least with respect to layout. I can't emphasize this enough, plan out what you want and document the steps to get there. I recommend a plugin called to-do-list. As I see things that need changing or fixing, I make an entry and if it's time sensitive assign it a due date. Having my to-dos in my admin area is so much more efficient than using Outlook or some other external task manager.
Another time saver is when you're customizing your layout, don't bog yourself down trying to get content posted just to see if the layout is right. Instead use Lorem Ipsum placeholders to test your layouts. Install a custom CSS plugin and learn some basic styling code. I use Add Custom CSS which allows me to modify styles site-wide or optionally per post or page and eliminates the need to modify the theme style sheet which would break when updated. Finally learn to use the browser's inspector to determine which selectors you need to modify to change the style. I use Firefox's inspector though Chrome's is equally useful.